Concerns came to light as Thurston was giving evidence to the Commons Transport Select Committee about the next steps for the £45bn phase one project.
He told MPs that police have had to be called on several occasions because of the risks.
Thurston said: “We’ve seen action by protesters that is anything but complying with the social distancing guidelines that the Government has advised.
“They’ve put our operatives at risk. We’ve had to engage security organisations to protect our sites and protect our operatives.
“In a number of instances the police have even been called, which frankly is not a great use of the police at this time.”
Thurston told the committee that around 75% of its 200 sites between London and Birmingham were now open.
He added: “Frankly, if we can’t comply with the guidelines we will shut our sites. We will take a zero-tolerance approach with our contractors.
“Our contractors are ultimately responsible for complying with the guidelines. I’ve engaged with all of the CEOs of our key contractors. They take this very seriously.”